.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/privacy/networks/plot_01_chaum_mix_nets.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_privacy_networks_plot_01_chaum_mix_nets.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_privacy_networks_plot_01_chaum_mix_nets.py:


Chaum's mix-nets: untraceable mail (1981)
=========================================

David Chaum wanted to hide who writes to whom, even from someone watching
every wire. A sender wraps its message in one layer of encryption per
*mix*, innermost for the last. Each mix collects a batch, removes one
layer from every message, and sends them on in a random order. The bytes
change at every hop and so does the order, so an observer cannot match
what goes in to what comes out.

Following a message needs every mix's shuffle. If the mixes are
:math:`M_1, \dots, M_k` and the observer learns the permutations of the
corrupt ones, a sender stays hidden among the whole batch as soon as one
mix is honest:

.. math::

   \Pr[\text{link}] = \begin{cases} 1 & \text{all mixes corrupt,} \\
   1/n & \text{otherwise, for a batch of } n. \end{cases}

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python

    from random import Random

    import matplotlib.pyplot as plt

    import blockchainkit as bk








.. GENERATED FROM PYTHON SOURCE LINES 31-34

Wrapping and peeling
--------------------
Each mix learns only the next hop.

.. GENERATED FROM PYTHON SOURCE LINES 34-42

.. code-block:: Python


    mixes = [bk.privacy.MixNode(f"mix{i}", 1_000 + i) for i in range(3)]
    onion = bk.privacy.wrap(b"meet at noon", mixes, "bob", Random(1))
    for mix in mixes:
        hop, onion = mix.peel(onion)
        print(f"{mix.name} forwards {len(onion):>3} bytes to {hop}")
    assert onion == b"meet at noon"





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    mix0 forwards  39 bytes to mix1
    mix1 forwards  25 bytes to mix2
    mix2 forwards  12 bytes to bob




.. GENERATED FROM PYTHON SOURCE LINES 43-46

A batch through the cascade
---------------------------
Eight senders write to eight recipients at once.

.. GENERATED FROM PYTHON SOURCE LINES 46-75

.. code-block:: Python


    rng = Random(2)
    onions = [bk.privacy.wrap(f"note {i}".encode(), mixes, f"r{i}", rng) for i in range(8)]
    run = bk.privacy.mix_cascade(onions, mixes, seed=3)
    print("delivered:", [recipient for recipient, _ in run.delivered])
    for sender in range(8):
        assert run.delivered[run.output_of(sender)][0] == f"r{sender}"

    corrupt_sets = {
        "none": frozenset(),
        "mix0": frozenset({0}),
        "mix0, mix2": frozenset({0, 2}),
        "all three": frozenset({0, 1, 2}),
    }
    candidates = {
        name: sum(len(run.candidates(s, corrupt)) for s in range(8)) / 8
        for name, corrupt in corrupt_sets.items()
    }
    print(candidates)
    assert candidates["mix0, mix2"] == 8 and candidates["all three"] == 1

    fig, ax = plt.subplots(figsize=(7, 3.5))
    ax.bar(list(candidates), list(candidates.values()), color="#2563eb")
    ax.set(xlabel="mixes that reveal their shuffle", ylabel="possible recipients per sender")
    ax.set_title("One honest mix hides each sender among the whole batch")
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/privacy/networks/images/sphx_glr_plot_01_chaum_mix_nets_001.png
   :alt: One honest mix hides each sender among the whole batch
   :srcset: /api/gallery/privacy/networks/images/sphx_glr_plot_01_chaum_mix_nets_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    delivered: ['r4', 'r3', 'r6', 'r1', 'r2', 'r5', 'r0', 'r7']
    {'none': 8.0, 'mix0': 8.0, 'mix0, mix2': 8.0, 'all three': 1.0}




.. GENERATED FROM PYTHON SOURCE LINES 76-82

Exercise
--------
The observer watches the cascade at a quiet hour, when only two
messages pass. What is the chance of linking a sender now, and what did
Chaum propose to keep batches large?
A worked solution is in :doc:`/exercises/privacy`.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.058 seconds)


.. _sphx_glr_download_api_gallery_privacy_networks_plot_01_chaum_mix_nets.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/privacy/networks/plot_01_chaum_mix_nets.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_chaum_mix_nets.ipynb <plot_01_chaum_mix_nets.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_chaum_mix_nets.py <plot_01_chaum_mix_nets.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_chaum_mix_nets.zip <plot_01_chaum_mix_nets.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_